Prime p₀= 2501408887789086311 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 112 2 58 2 76 2 16 2 40 2 (?)
a_n: 0 2 36 38 150 152 210 212 288 290 306 308 348 350
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 350
Found by: Groo
db: batch=82, k=14, 34 112 58 76 16 40

SPT(16)	2501407534039542833	0 20 80 90 146 158 174 224 420 470 486 498 554 564 624 644	-1353749543478
SPT(16)	2501407758394363997	0 24 62 66 104 114 132 146 150 164 182 192 230 234 272 296	-1129394722314
SPT(16)	2501408175942572159	0 2 32 42 60 170 182 200 222 240 252 362 380 390 420 422	-711846514152
STPT(10)	2501408333680417487	0 2 30 32 42 44 54 56 84 86	-554108668824
SPT(16)	2501408552915338301	0 2 20 96 110 138 146 152 156 162 170 198 212 288 306 308	-334873748010
STPT(10)	2501408803410246407	0 2 30 32 42 44 54 56 84 86	-84378839904
STPT(10)	2501408910075176081	0 2 36 38 78 80 120 122 156 158	22286089770
STPT(10)	2501409167895148739	0 2 42 44 90 92 138 140 180 182	280106062428
TPT(14)	2501409205183345319	0 2 18 20 78 80 90 92 102 104 132 134 168 170	317394259008
STPT(10)	2501409512125858517	0 2 30 32 42 44 54 56 84 86	624336772206
SPT(16)	2501409860372423417	0 30 62 102 114 120 132 140 204 212 224 230 242 282 314 344	972583337106